Let us briefly explain the values of the table. By work of Oliver [1]}, the kernels \(SK_1(R_j)\)  of the determinant maps are trivial, and hence (see for example [2]}) \(K_1(R_j)\)  is the group of units of \(R_j\) . Now the values of \(K_1\)  follow from a theorem of Higman ([3]}, see also [4]}). In turn, by [5]}, the reduced \(K_0\)  of these three rings is trivial, and then [6]} implies that \(K_0(R_j)=\mathbb {Z}\)  for every \(j\) . The values of the third column follow from work of Carter [7]}, being the figures \(r\)  and \(s\)  positive integers that depend on the Schur indexes. Finally, the Nil-terms of the two last columns were computed by Weibel in [8]}.
